Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ
14.3 EVALUATION OF A NEW MULTIPLE-DOPPLER TORNADO DETECTION AND CHARACTERIZATION TECHNIQUE USING REAL RADAR OBSERVATIONS
Corey K. Potvin* ,1 , Alan Shapiro 1, Tian-You Yu 2, and Jidong Gao 3 1School of Meteorology, University of Oklahoma, Norman, OK 2School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 3Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, OK
1. INTRODUCTION tive Adaptive Sensing of the Atmosphere; Mclaughlin et al. 2005; Brotzge et al. 2007) radar Since the implementation of the WSR-88D network to detect small-scale vortices and also to network, several algorithms have been developed provide vortex characteristic estimates which may to aid forecasters in real-time identification of in- improve tornado nowcasting. The vortex para- tense small and mesoscale vortices. The National meters are obtained by minimizing a cost function Severe Storms Laboratory (NSSL) Mesocyclone which measures the discrepancy between the ob- Detection Algorithm (MDA; Stumpf et al. 1998) served and model radial wind fields. By taking the was designed to alert forecasters to the presence translation of the system into account, the radar of supercell thunderstorms, which produce a large data can be used at their actual locations and portion of tornadoes in the United States. The times of acquisition. NSSL Tornado Detection Algorithm (TDA; Mitchell Tests of the technique using analytically- et al. 1998) calculates azimuthal shear of radial generated and numerically-simulated tornadic wind using adjacent radar resolution volumes, and wind fields can be found in Potvin et al. (2008). In identifies regions where shear exceeds a thre- this paper, the technique is applied to real dual- shold. Unfortunately, the success of the TDA al- Doppler observations of tornadoes. The low-order gorithm and others of its kind [e.g., Tornado Vor- model is introduced in section 2. The computation tex Signature (TVS) algorithm, Crum and Alberty and minimization of the cost function is described 1993] depends upon the chosen detection thre- in section 3. Section 4 describes tests using sholds, the suitability of which is largely range- WSR-88D observations of an F4 tornado which and storm-dependent. Thus, this approach may struck central Oklahoma on 8 May 2003. Section be subject to high false alarm rate or low probabili- 5 describes tests using high-resolution Doppler- ty of detection values. on-Wheels observations of a relatively small tor- The Velocity Track Display (VTD) technique nado. A summary and plans for future work follow and its variants (Lee et al. 1994; Roux and Marks in section 6. 1996; Lee et al. 1999; Liou et al. 2006) were de- veloped to retrieve the three-dimensional velocity field of a specific class of meteorologically signifi- 2. DESCRIPTION OF LOW-ORDER MODEL cant flows: intense vortices. These techniques fit radial velocity data to a vortex model in order to The low-order model used in this study is recover key characteristics of the vortex flow. This comprised of four idealized flow fields: a uniform capability distinguishes this approach from tradi- flow, linear shear flow, linear divergence flow, and tional dual-Doppler analysis, which does not con- modified combined Rankine vortex (MCRV; strain the retrieved wind field with a spatial vortex representing the tornado). The vortex and its envi- model and thus is not designed to retrieve vortex ronment are allowed to translate. Our use of the characteristics. Our method also adopts a vortex- MCRV model is supported qualitatively by high- fitting approach. More specifically, radial wind ob- resolution mobile radar observations of tornadoes servations from two or more close-proximity Dopp- whose azimuthally-averaged tangential winds ler radars with overlapping domains are fit to an roughly followed this profile (Wurman and Gill analytical low-order model of a vortex and near- 2000; Bluestein et al. 2003; Lee and Wurman environment. The model control parameters in- 2005). clude vortex location, size, intensity, and transla- The Cartesian components of the linear flow tion velocity. Our method is designed to capitalize fields (broadscale flow) are given by upon the increased observational density and overlapping coverage of a CASA-like (Collabora-
1 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ
Vx=+ a by( − vt b ) + cx ut), ( b To facilitate calculation of the radial (with re- (1) spect to a radar) component of the model wind V=+ d ex( − ut ) + fy vt ( ), y b b fields, the Cartesian components of the model wind fields are first obtained and then the radial where a, d are constant flow components, b, e are component is extracted. Toward that end, the ve- shear parameters, c, f are divergence parameters, locity V of the MCRV can be expressed in vortex- ub, vb are the translational velocity components of centered cylindrical coordinates (not radar coordi- the broadscale fields, and t is time. It can be nates) as the sum of its radial and tangential com- noted that (1) implicitly makes provision for a ponents, V ˆ ˆ , where ˆ and ˆ are the broadscale vortex since the Cartesian representa- =vr r + v θθ r θ tion of a solid body vortex is u=− y,v = x, unit vectors in the radial and azimuthal directions in the vortex cylindrical coordinate system, respec- where is the (constant) vortex angular velocity. tively. Figure 1 depicts the relationship between This broadscale vortex description is independent the Cartesian and vortex coordinate systems. The of the small-scale vortex model to be described Cartesian components of V are computed as: next. In a local cylindrical coordinate system cen- ˆ V tered on and translating with the modified com- u=⋅= i vcosr θ − vsinθ θ , ˆ V bined Rankine vortex, the azimuthal velocity field v=⋅= j vsinr θ + vcosθ θ . (4) vθ and radial velocity field vr are given by: Formulae for cosθ and sinθ at arbitrary time t fol- r r low immediately from Fig. 1: V,T r< R, V,R r< R, R R vθ = vr = (2) Rα Rβ x− x0 − utv V, r≥ R, V, r≥ R, cos θ = , α T β R r r r y− y − vt where sin θ = 0 v . r 2 2 r=( xxut −−0v )( +−− yy 0 vt v ) , (3) Substituting these into (4) yields is the distance of a given ( x, y) coordinate from the xx−− ut yy −− vt u=0v v − 0 v v , center of the vortex at time t. The vortex is de- rr r θ scribed by seven parameters: initial vortex center yy−−0 vtv xx −− 0 ut v location ( x0, y0), radius of maximum wind R, max- v= v + v . rr r θ imum tangential velocity VT, maximum radial ve- Substituting for vr, vθ from (2) and adding the linear locity VR, the radial decay rates α, β of the tangen- tial and radial wind components, and the transla- flow fields (1) produces the Cartesian representa- tion of the full model wind field: tional velocity components uv , v v. The model pa- rameters are listed in Table 1. ______
VR V T ab(yvt)c(xut)+−+−+bb (x −−− x0 ut) v (y −− y 0 vt), v r < R, R R u = β α RV(xR−− x0 ut) v RV(y T −− y 0 vt) v a+−+−+ b(y vt)b c(x ut) b −, r ≥ R, rβ+1 r α + 1
VR V T v=+−+−+ d e(xut)bb f(yvt) (y −−+ y0 vt) v (xx −− 0 ut), v r < R, R R v = β α RV(yR−− y0 vt) v RV(x T −− x 0 ut) v =+−+−+d e(x ut)b f(y vt) b +, r ≥ R. rβ+1 r α + 1
mod Finally, solving for the radial component of the total velocity yields the model Doppler radar velocity, Vr :
2 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ
mod VR V T Vrnnbb= cosφ sin θ a +−+−+ b(y vt)c(xut) (x −−− x0 ut) v (y −−+ y 0 vt) v R R VR V T cosφnnbb cos θ d+−+−+ e(x ut) f(y vt) (y −−+ y0 vt) v (x −− x 0 ut) v R R r< R, (5) RV(xβ−− x ut) RV(y α −− y vt ) =cosφ sin θ a +−+−+ b(y vt) c(x ut) R0 v − T 0 v + nn b b β +1 α +1 r r RV(yβ−− y vt) RV(x α −− x ut) cosφ cos θ d+−+−+ e(x ut) f(y vt) R0 v + T 0 v nn b b β+1 α + 1 r r r≥ R. ______
where θn and φn are the azimuth and elevation an- normalized, can be used to calculate the mean th gles, respectively, of the n radar ( θn is measured model error per radar grid point. clockwise from the north). The cost function J is minimized to retrieve the set of parameter values producing the least 3. COST FUNCTION COMPUTATION AND squares error in the model wind (best fit between MINIMIZATION model and observed winds). In view of (6) and the location of the model parameters in (5), our mini- The (squared) discrepancies between the ob- mization problem is highly non-linear. Conjugate served and model-predicted radial wind fields are gradient minimization methods have proven useful summed over the spatial-temporal domains of N for such problems. The minimization algorithm radars, each scanning in range rn, azimuth θ and used in this technique is the Polak-Ribiere (1969) elevation angle φ. By taking the translation of the method, a robust and efficient variant of the broadscale flow and vortex into account, discre- Fletcher and Reeves (1964) algorithm. In both pancy calculations for the radial wind model can methods, the search direction is reset to that of be performed at the same locations and times as steepest descent (with all previous direction and the observations. gradient information being discarded) every p ite- Since radar resolution volumes increase in rations, where p is the number of model parame- size with distance from the radar, Doppler velocity ters. observations become representative of winds over As with other minimization techniques, mul- a larger region as range increases. A range- tiple minima in J can prevent the global minimum 2 2 weighting factor, rn /r mean , is introduced to account from being reached. Local minima in the current for this. problem can result from the intrinsic non-linearity The cost function J accounting for the discre- of the problem, as well as from areas of missing pancies between the observed and model- data and departures of the observed wind field predicted radial wind fields is from the model. An important example of the latter occurs M 2 when a tornado is collocated with a larger, non- rn obs mod 2 tornadic vortex such as a mesocyclone. In such J≡ [ (VV)] − , ∑ ∑∑∑∑ r r r cases, the non-tornadic circulation, by virtue of its n=1 m = 1 φ θ r mean n larger “footprint”, may fit the low-order model bet- (6) ter than the tornado itself, thus preventing the tor- nado from being detected. In order to address this where M is the total number of full volume scans problem, the minimization procedure was split into (temporal sum) and rn is the radial distance of a th two steps. Figure 2 illustrates the procedure using point from the n radar (the range-weighting factor one of the tests with numerically-simulated data is appropriately modified in experiments with real described in Potvin et al. (2008). In step 1, the data as described above). J provides a useful way vortex model parameters are fixed at zero (except to quantitatively compare the quality of retrievals for R since this would introduce a “division by ze- for different experiments, and, when appropriately ro” computational issue), and the broadscale pa- 3 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ rameters are retrieved. In step 2, the radial com- 4.2. Selection of analysis domains ponents of the wind field retrieved in step 1 are subtracted from the observed radial wind fields, Using enough analysis domains to cover the and the retrieval is repeated on the residual wind entire dual-Doppler domain would, in the absence field. Since the flow retrieved in step 1 (and sub- of a high performance computing cluster, require tracted in step 2) is much more representative of too much time for the technique to be applied ope- the broadscale flow than of the tornadic flow, the rationally. Therefore, the technique was modified tornadic component of the original flow dominates so that retrievals are performed only in regions the residual field to be retrieved in step 2. identified as possibly containing tornado-like vor- In order to further mitigate the problem of mul- tices. The process by which these regions are tiple minima, retrievals are performed for a multi- selected begins by identifying all pairs of azimu- tude of first guess vortex centers. This increases thally-adjacent radar gates which satisfy the fol- the probability of detecting any tornadoes present lowing criteria: (1) azimuthal shear of radial veloci- within the analysis domain. ty calculated between the two radar gates exceeds .05 s -1; (2) the azimuthal distance between the two gates is less than 1 km; (3) radial velocity exceeds 4. TESTS WITH WSR-88D OBSERVATIONS OF 25 m s -1 in at least one of the gates; and (4) < 20 8 MAY 2003 OKLAHOMA CITY TORNADO % of the velocity data is missing within both 500 m and 1000 m of each of the gates. Criteria 1, 2 and 4.1. Description of Dataset 3 are intended to distinguish between tornado-like vortices and weaker or broader vortices. Criterion On 8 May 2003, a supercell produced a long- 4 was partly motivated by analytical experiments lived F4 tornado in the southern portion of the Ok- in which velocity data gaps produced spurious mi- lahoma City, Oklahoma metropolitan area. The nima in J. tornado remained within the dual-Doppler domain For each pair of radar gates satisfying all four of the KOKC (a Terminal Doppler Weather Radar) criteria, the centroid of the two gates is stored. and KTLX radars (characteristics of both radars Since vortices always exhibit azimuthal shear sig- are listed in Table 2) throughout its lifetime, during natures in the velocity fields of both radars, all which 0.5 ° elevation reflectivity and radial velocity centroids which are located within 2 km of another scans were performed every ~5 min by KTLX and centroid in the other radar’s domain are retained. every ~1 min by KOKC. The tornado damage All such points are then spatially grouped into path and relative locations of KOKC and KTLX are clusters (since there may be multiple proximate depicted in Figure 3. A set of retrieval experiments points associated with the same vortex) whose was performed using data from five consecutive centroids are calculated and stored. Each centro- id corresponds to the center of a region over which 0.5 ° KTLX scans along with one 0.5 ° KOKC scan the retrieval technique will be applied. A grid of taken within ~30-60 s of each KTLX scan. All ve- nine first guesses (spacing = 500 m) for the vortex locity data used in the experiments were subjec- center (each serving as the center of an analysis tively de-aliased. The proximity of the tornado to domain over which the retrieval is applied) is sub- both radars (11-26 km) allowed observations to be collected at an azimuthal resolution characteristic sequently calculated and input to the retrieval rou- tine. of a CASA network. However, the range resolu- For each of the observational periods in this tion of these data (150 m and 250 m) is coarser set of experiments, the only set of analysis do- than that for a CASA radar (~50-100 m), and the mains to be objectively selected for input to the large time interval between KTLX 0.5 ° scans re- retrieval routine contained the tornado. Each set quired that retrievals be performed on single pairs of nine retrievals required less than 1 min of com- of KTLX/KOKC scans rather than using multiple putational time on a single AMD 2.6 GHz Opteron consecutive scans from each radar. Thus, the processor. It is currently unknown whether the retrievals obtained in these experiments are pre- analysis domain selection criteria are (or can be sumably representative of, or somewhat poorer modified to be) sufficiently robust to simultaneous- than, those which would have been obtained had ly maintain a low number of retrieval sets and a the tornado been sampled by a network of CASA high probability of detection over a wide range of radars. tornado scenarios. If a large number of retrievals
are needed, then parallel processing (one proces-
sor for each set of analysis domains) could be
4 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ used to produce acceptable computational wall 3), which together spanned most of the tornado’s clock times. lifetime. The mean distance between the vortex centers retrieved during each observational period 4.3. Detection criteria and vortex characterization (excluding the last period, during which only one detection was made) ranged from 57 m to 201 m, It was found in Potvin et al. (2008) that proxim- indicating that the technique was not unduly sensi- ity of a vortex to a data boundary can result in spu- tive to errors in the first guess vortex center. rious minima. This problem occasionally resulted Though direct comparison of the mean re- in the retrieval of spurious vortices in preliminary trieved vortex centers and R30 values to the ob- experiments with real data (not shown). There- served damage path is hindered by several is- fore, in the experiments described below, retriev- sues, most notably that the analysis domains in als were rejected if the magnitude of the retrieved these experiments are ~ 100-220 m above the ground, the results are nevertheless encouraging. vortex wind =v2 + v 2 exceeded 20 m s -1 at ( r θ ) The mean retrieved vortex centers are all very nearly collocated with the observed tornado dam- the edge of the analysis domain. age path (Figure 3). The mean retrieved R for A retrieved vortex is identified as a tornado if α 30 -1 each of the experiments are (in chronological or- < 1.0 and the radius of 30 m s tangential winds, der) 248 m, 296 m, 318 m, 265 m and 307 m, R , exceeds 200 m. The latter threshold is ob- 30 consistent with the observed maximum damage tained by taking the mean of the smaller sampling path width of ~ 650 m. The trend of R is similar interval for each radar (150 m and 250 m for 30 to that of the damage path during the first four ob- KOKC and KTLX, respectively). The other crite- servational periods, while the fifth estimate is too rion was motivated by the occasional retrieval of large. spurious vortices having unrealistically large (> In order to assess how well the low-order 1.0) values of α. Such a rapid decline in v with θ model was able to reproduce the complexity of the distance from the vortex center violates the Ray- input radial velocity fields, the mean retrieved wind leigh (1916) instability condition and therefore may field was compared to the observed wind field not be sustainable in actual tornadoes. This hypo- within the central analysis domain in each experi- thesis is supported by high-resolution observa- ment. A representative comparison (experiment # tional studies of tornadoes (e.g. Wurman and Gill 3) is shown in Figure 4. Naturally, the low-order 2000; Lee and Wurman 2005; Wurman and Alex- model is unable to completely recover the intricate ander 2005) which have found that α typically va- structure of the near-tornado radial wind field. ries between 0.6 and 0.8. However, the retrieved wind field does reasonably The mean retrieved vortex center and R30 are capture the primary structure of the tornado, at computed from the retrievals performed within least on the scale of the observational data. each set of analysis domains. The latter parame- ter is intended to provide a useful estimate of the radius of damaging winds in the tornado. Mean 5. TESTS WITH DOPPLER-ON-WHEELS retrieved values of R and VT (as well as the re- OBSERVATIONS OF 5 JUNE 2001 ATTICA, KS maining model parameters) are also calculated, TORNADO but the tornado was not sufficiently resolved in these experiments for these estimates to be relia- ble. Since multiple tornado-like vortices may exist 5.1. Description of Dataset within a single set of analysis domains, the tech- nique is designed such that retrieved vortices The technique was next applied to a dual- passing the detection criteria which are located > 1 DOW (Doppler on Wheels; Wurman et al. 1997) km from the remaining detections have their cha- dataset of a relatively small tornado which oc- racteristics calculated separately. In the experi- curred near Attica, KS on 5 June 2001. Due to the ments presented herein, the technique correctly presence of intervening precipitation, the tornado identifies a single tornado. was never visually observed by the DOW team, and so the precise time period(s) during which the 4.4. Results tornado occurred is unknown. The peak intensity of the tornado is also uncertain since no damage The technique successfully detected the tor- survey was performed. The vortex was estimated nado during all five observational periods (Table by a sheriff to be around 100 m in diameter,
5 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ though it is possible the tornado widened and/or 5.3. Results narrowed during times in which it was not ob- served. Tornado detections were made at all of the The azimuthal sampling interval for both ra- eight times for which the algorithm was performed dars averaged less than 0.4° and the radial sam- (Table 3). Again, it is not known at which times a pling interval varied between 50 m and 75 m. Due tornado was actually occurring, however, inspec- to the very high observational density the radius of tion of the observed radial wind fields, some of 25 ms -1 vortex tangential wind, R25, was used in which are shown in Figure 5, indicates that an in- the detection criteria rather than R30. Since the tense vortex was indeed present at most or all of azimuthal spacing between observations was typi- these times. The retrieved radial velocity fields cally less than the radial spacing, the detection generally compare favorably to the observations, threshold for R25 was set to the mean azimuthal although relatively poor broadscale flow retrievals spacing between observations (rather than the may have prevented the most intense vortex in the mean radial spacing as in the previous set of ex- analysis domain from being detected at time # 8. periments) within the analysis domain. The azi- Both the retrieved radial velocity fields and plots of muthal distance between observations near the retrieved V T and R 25 over time (Figure 6) indicate tornado averaged around 50 m. that the algorithm captured trends in the size and The technique was applied to a single pair of resolvable intensity of the vortex reasonably well. radial velocity PPI scans for eight consecutive Due to the large values of radial velocity and coordinated pairs of volume scans. Each pair of shear present over a large area of the storm, the PPIs was selected such that the heights of the algorithm frequently performed retrievals in re- radar beams were within 100 m of each other in gions located well away from the suspected torna- the vicinity of the tornado. The heights of the PPIs do. No detections were made in these cases ex- near the tornado were typically ~ 100-150 m AGL cept at time # 7. Inspection of the radial wind in these cases. fields at this time reveals that an anticyclonic vor- tex may indeed be present at the location of the 5.2. Modifications to Technique detection (Figure 7). The observational resolution in these experi- In this set of tests, the low-order model was ments is admittedly higher than in a typical CASA- expanded to account for vertical shear of the like radar network. However, it should be borne in broadscale flow. This is because the variation in mind that the tornado being retrieved is relatively height over the analysis domain in some of these small (Alexander and Wurman 2008). Thus, the experiments was potentially significant due to the technique’s ability to detect the tornado and cha- proximity of the tornado to one of the radars. racterize trends in its size and strength is encour- During our experiments it was found that, even aging. away from data boundaries, the technique occa- sionally retrieves an intense vortex where none is 6. SUMMARY AND FUTURE WORK actually present in the data (not shown). Curious- ly, such spurious vortex retrievals tend to occur in A new multiple-Doppler technique for identify- regions of relatively weak flow. Therefore, in order ing and characterizing tornadoes has been pre- to filter these false detections, vortices retrieved in sented. The method consists of fitting radial wind regions in which (1) the maximum absolute Vr observations to a low-order model of a tornado- measured by both radars is less than 20 ms-1, or like vortex and its near environment. The tech- (2) the maximum absolute Vr measured by one nique takes advantage of the enhanced density radar is less than 15 ms-1, or (3) the maximum (and therefore spatial coverage and resolution) of gate-to-gate radial wind difference is less than 10 a CASA-like radar network. The retrieval tech- ms-1 are automatically rejected by the algorithm. nique has previously been tested against analyti- This is admittedly a rather ad-hoc solution to this cally-generated observations as well as a high- problem. It is hoped that the cost function can be resolution ARPS simulation of a tornado and sur- modified (perhaps, for example, by incorporating rounding wind field (not shown). In this work, the spectrum width data) to prevent these spurious algorithm was applied to two sets of real dual- vortex retrievals. Doppler observations of a tornado. The technique exhibits skill not only in detecting tornado-like vor- tices within a CASA-like network, but also in re- trieving the vortex location and wind field on
6 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ scales greater than or equal to that of the radar McGrath, Kevin Scharfenberg, Herb Stein, Josh grid. Characteristics of retrieved vortices, if avail- Wurman and Pengfei Zhang during ROTATE (Ra- able to forecasters in real-time, could aid in the dar Observations of Tornadoes and Thunders- tornado warning process. torms Experiment) 2001. The work presented Spurious minima can pose a serious threat to herein was primarily supported by NSF grant EEC- the algorithm’s ability to converge to the correct 031347, through the Engineering Research Center minimum, especially when the first guess model (ERC) for Collaborative Adaptive Sensing of the parameters (particularly the location of the vortex Atmosphere (CASA). center) contain significant error. Boundary minima in J(x0, y 0) can occur near the edge of the analysis domain, and local minima can occur in other multi- REFERENCES dimensional cross-sections of J due to regions of missing data or deviations of the observed wind Alexander, C., and J. Wurman, 2008: Updated pattern from that described by the low-order mod- mobile radar climatology of supercell tornado el. An important special case of such a deviation structures and dynamics. Preprints, 24 th Conf. is the presence of multiple vortices in the data. on Severe Local Storms, Savannah, GA, This local minima problem necessitates the use of Amer. Meteor. Soc. multiple first guesses for the location of the vortex Bluestein, H. B., W.-C. Lee, M. Bell, C. C. Weiss, and of a two-step approach in which much of the and A. L. Pazmany, 2003: Mobile Doppler ra- larger-scale flow is retrieved and subtracted before dar observations of a tornado in a supercell a small-scale vortex retrieval is performed. The near Bassett, Nebraska, on 5 June 1999. Part latter strategy is necessary in cases where a II: Tornado-vortex structure. Mon. Wea. Rev ., weaker and broader vortex-like circulation pro- 131 , 2968–2984. vides a better fit to the low-order model over an Brotzge, J., K. Brewster, V. Chandrasekar, B. Phi- analysis domain than a collocated intense vortex. lips, S. Hill, K. Hondl, B. Johnson, E. Lyons, D. Finally, the stationarity of the low-order model pa- McLaughlin, and D. Westbrook, 2007: CASA rameters requires that the temporal analysis do- IP1: Network operations and initial data. Pre- main be limited in order to mitigate violation of the prints, 87 th AMS Annual Meeting, San Antonio, model in cases of rapid flow evolution. TX, Amer. Meteor. Soc. Successful detection and characterization cri- Crum, T. D., and R. L. Alberty, 1993: The WSR- teria (to be further developed in future work) need 88D and the WSR-88D Operational Support to account for non-uniqueness in the vortex para- Facility. Bull. Amer. Meteor. Soc ., 74 , 1669– meters due to finite observational resolution and 1687. the mathematical nature of the low-order model. Fletcher, R., and C.M. Reeves, 1964: Function One preliminary approach tested herein is the in- minimization by conjugate-gradients. Comput clusion in the detection criteria of retrieved vortex er J. , 7, 149-153. characteristics which are resolvable on larger Lee, W.C., and F.D. Marks, 2000: Tropical Cyc- scales than the vortex core. This approach dem- lone Kinematic Structure Retrieved from Sin- onstrated skill in distinguishing between tornadic gle-Doppler Radar Observations. Part II: The and spurious retrieved tornado-like vortices in our GBVTD-Simplex Center Finding Algorithm. experiments. Mon. Wea. Rev ., 128 , 1925–1936. Due to computational constraints, it is not ——, W.-C., and J. Wurman, 2005: Diagnosed possible to apply the technique over the entire three-dimensional axisymmetric structure of multiple-Doppler radar domain in real-time. Objec- the Mulhall tornado on 3 May 1999. J. Atmos. tive radial velocity criteria were therefore devel- Sci ., 62 , 2373-2393. oped to identify sub-domains possibly containing ——, F. D. Marks, Jr., and R. E. Carbone, 1994: tornadoes. These criteria will be further tested Velocity Track Display – A technique to extract and refined through additional tests with real mul- real-time tropical cyclone circulations using a tiple-Doppler tornado observations. single airborne Doppler radar. J. Atmos. Oceanic Technol ., 11 , 337–356. ——, J.-D. Jou, P.-L. Chang, and S.-M. Deng, Acknowledgements: We appreciate the contribu- 1999: Tropical cyclone kinematic structure re- tions of the Doppler on Wheels crew including trieved from single Doppler radar observa- Curtis Alexander, MyShelle Bryant, Bob Conze- tions. Part I: Interpretation of Doppler velocity mius, David Dowell, Steve McDonald, Kevin
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patterns and the GBVTD technique. Mon. radar. J. Atmos. Oceanic Technol. , 14 , 1502– Wea. Rev. , 127 , 2419-2439. 1512. Liou, Y.-C., T.-C. Chen Wang, W.-C. Lee, and Y.- J. Chang, 2006: The retrieval of asymmetric tropical cyclone structures using Doppler radar simulations and observations with the Ex- tended GBVTD technique. Mon. Wea. Rev ., 134 , 1140-1160. McLaughlin, D., V. Chandrasekar, K. Droegemei- er, S. Frasier, J. Kurose, F. Junyent, B. Phi- lips, S. Cruz-Pol, and J. Colom, 2005: Distri- buted Collaborative Adaptive Sensing (DCAS) for improved detection, understanding, and predicting of atmospheric hazards. Preprints, 85 th AMS Annual Meeting, San Diego, CA, Amer. Meteor. Soc. Mitchell, E. D., Vasiloff, S. V., Stumpf, J. G., Witt, A., Eilts, M. D., Johnson, J. T., and K. W. Thomas, 1998: The National Severe Storms Laboratory Tornado Detection Algorithm. Wea. Forecasting , 13 , 352–366. Polak, E. And G. Ribiere, 1969: Note sur la convergence de methods de directions conjuguees. Rev. Franc. Informat. Rech. Operationnelle, 16 , 35-43. Potvin C. K., Shapiro A., Yu T.-Y., Gao J., and Xue M., 2008: Using a low-order model to detect and characterize tornadoes in multiple- Doppler radar data. Mon. Wea. Rev ., In Press. Rayleigh, Lord (J. W. Strutt), 1916: On the dynam- ics of revolving flows. Proc. Roy. Soc. London, A93, 148-154. Roux, F., and F. D. Marks, 1996: Extended veloci- ty track display (EVTD): An improved processing method for Doppler radar observa- tion of tropical cyclones. J. Atmos. Oceanic Technol. , 13 , 875–899. Wurman, J., and S. Gill, 2000: Finescale radar observations of the Dimmitt, Texas (2 June 1995), tornado. Mon. Wea. Rev ., 128 , 2135- 2164. ——, and C. R. Alexander, 2005: The 30 May 1998 Spencer, South Dakota, Storm. Part II: Comparison of observed damage and radar- derived winds in the tornadoes. Mon. Wea. Rev. , 133 , 97–119. ——, Y. Richardson, C. Alexander, S. Weygandt, and P.-F. Zhang, 2007a: Dual-Doppler and single-Doppler analysis of a tornadic storm undergoing mergers and repeated tornadoge- nesis . Mon. Wea. Rev ., 135 , 736–758. ——, J. Straka, E. Rasmussen, M. Randall, and A. Zahrai, 1997: Design and deployment of a portable, pencil-beam, pulsed, 3-cm Doppler
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Table 1. Low-order model parameters.
Param eter Description a (m s -1) Uniform flow d (m s -1) b (s -1) Shear amplitudes e (s -1) c (s -1) Divergence amplitudes f (s -1) -1 ub (m s ) -1 Broadscale field translation vb (m s ) R (m) Radius of max wind -1 VR (m s ) -1 Max radial, tangential wind VT (m s ) x (m) 0 Vortex center y0 (m) -1 uv (m s ) -1 Vortex translation vv(m s ) α Vortex wind decay β
Table 2. Selected characteristics of the KOKC and KTLX radars.
Doppler Beamwidth Azimuthal Sa m- Range Sampling Band pling KTLX S 0.95 ° 1.0 ° 250 m KOKC C 1.0 ° 1.0 ° 150 m
Table 3. Number of tornado detections (out of nine retrievals) made in each of the May 8 2003 and 5 June 2001 experiments.
Experiment Number of Detections 8 May 2003 # 1 5 # 2 4 # 3 4 # 4 3 # 5 1 5 June 2001 # 1 1 # 2 4 # 3 2 # 4 1 # 5 7 # 6 6 # 7 3 # 8 2
9 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ
Fig. 1. Cartesian and cylindrical (vortex) coordinate systems defin- ing model broadscale and vortex flows, respectively at t = 0. The vortex is initially located at x0, y 0.
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Wind Vectors (m/s) 6000 Wind Vectors (m/s) 6000
5500 5500
5000 5000
4500 4500 Y(km) Y(km)
4000 4000
3500 3500
max = 75 m/s max = 50 m/s 3000 3000 2500 3000 3500 4000 4500 5000 5500 2500 3000 3500 4000 4500 5000 5500 X (km) X (km)
Wind Vectors (m/s) 6000 Wind Vectors (m/s) 6000
5500 5500
5000 5000
4500 4500 Y(km) Y(km)
4000 4000
3500 3500
max = 64 m/s max = 61 m/s 3000 3000 2500 3000 3500 4000 4500 5000 5500 2500 3000 3500 4000 4500 5000 5500 X (km) X (km)
Fig. 2. Illustration of two-step retrieval procedure: (a) total wind field, (b) retrieved broadscale flow, (c) the vector difference (a)- (b), and (d) total retrieved flow.
11 Extended abstract AMS 89 th Annual Meeting 11 15 January 2009, Phoenix, AZ
Fig. 3. Location of the tornado damage path (F0+) relative to KTLX and KOKC. The dots along the dam- age path indicate the tornado locations retrieved by the technique. Radial Velocity (m/s) Radial Velocity (m/s) 15.5 50 15.5 50 15 40 15 40 30 30 14.5 14.5 20 20 14 14 10 10
13.5 0 13.5 0 Y (km) Y Y (km) Y -10 -10 13 13 -20 -20 12.5 12.5 -30 -30 12 12 -40 -40
11.5 -50 11.5 -50 10 11 12 13 10 11 12 13 X (km) X (km)
Radial Velocity (m/s) Radial Velocity (m/s) 9.5 50 9.5 50 40 9 9 40 30 30 8.5 8.5 20 20 8 8 10 10
7.5 0 7.5 0 Y (km) Y Y (km) Y -10 -10 7 7 -20 -20 6.5 6.5 -30 -30 6 6 -40 -40
5.5 -50 5.5 -50 -11 -10 -9 -8 -11 -10 -9 -8 X (km) X (km)
Fig. 4. KTLX (top left) and KOKC (bottom left) observed (left panels) vs. retrieved (right panels) radial velocities.
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Fig. 5. Observed (left panels) and retrieved (right panels) radial velocity for DOW2 (top panels) and DOW3 (right panels) at four of the eight times at which retrievals were performed.
Time # 2
Time # 4
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Time # 6
Time # 8
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Fig. 6. Retrieved R 25 and V T at eight consecutive times.
Fig. 7. Same as Fig. 5 except for a region located well away from the suspected tornado at time # 7.
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